We are what we do. For 40 years, I have been a scientist, mathematician, engineer, teacher, and
philosopher. A few years ago, I decided that it was time to celebrate and illustrate the depth
of my professional experiences and expertise by designing my own tattoos and wearing them on my
own canvas. I needed them to be unique to me so that they would tell my professional story as
well as being tastefully artistic. Fred "Outlaw" Whelan (of Body
Matrix in Bemidji MN) was instrumental in his suggestions and applying the finishing
touches to my original ideas and sketches for making the final designs artistic enough to be
worthy of permanent display.

Apparently, Fred and I succeeded in making the tattoos attractive to a great many people. Frequently,
during the warm weather months when I am wearing my trademark tank top and shorts attire, I get asked
about the tattoos: "Why are they so different from other people's tattoos?" "What do they mean (if
anything)?" "Where did you find those designs?" "Why did I do it?" "I thought only bikers and low
lifes have tattoos." This page is my response to some of the questions that are often asked, mostly
explaining what each tattoo means. Some of the other questions are best answered by going to Carl
Zimmer's Science
Tattoo Emporium (where my first two tattoos are featured
[here]),
to the RF Cafe, or to Zimmer's forthcoming book
Science Ink
(Fall 2011), which will also feature several of my tattoos.

What follows is the story and explanation of my ink:

After years of needling from my musician wife (who has a pair of music tattoos on her shoulders),
I finally took up the challenge in January 2009 and began wasting large amounts of time designing my
own science, engineering, and mathematics tattoos. I greatly enjoyed the time and effort to get them
just right, to reflect who I am and what I do (Professor of Physics and Engineering).

Photon in Flight

Periodic Table and Planck Snake

The right shoulder tattoo [above left] is a 3D perspective abstract view of a gaussian photon, a
"particle of light." The red vertical undulations represent the electric field, the black
horizontal undulations the magnetic field. It is propagating to the right, seen here as a
snapshot in time. The photon is the single most common manner in which information is transmitted
from one place in the universe to another. Fred Whelan, the tattoo artist, suggested adding the
faint shadows to give it depth, but the real reason I agreed to the shadowing was the ironic
(oxymoronic?) humor of a particle of light casting a shadow.

The left shoulder tattoo [above right] is a 3D perspective of the Periodic Table with the Planck Snake
weaving around it (note the h-bar, Planck’s constant, in the eye). The snake represents the wave
nature of matter, and Physics in general. (The infinity symbol the snake forms is a bonus.) The
combination of the Periodic Table of Chemistry with the Planck Snake of Physics is also an inside
joke at the expense of chemists: It took the Quantum Mechanics of Physics to explain to Chemistry
its own Table of Elements.

Hertzsprung-Russell Diagram

Hertzsprung-Russell Diagram Scatter Plot

The right upper arm tattoo [above left] is an abstract representation (in a tribal motif) of the Hertzsprung-Russell
Diagram of Astronomy. The H-R Diagram is a scatter plot [above right] of the surface temperature vs. absolute
brightness of all the visible Stars in the Milky Way Galaxy. The design here also suggests the
sweeping paths that aging Stars follow as they evolve during their lifetimes. The eight-point star
represents our Sun, in the band (called the Main Sequence) that extends diagonally from the upper
left corner to the lower right. The regions above and below represent Red Giant and White Dwarf
stars, resp. Our sun will pass through the Red Giant stage on its way to becoming a White Dwarf
in about five billion years.

Strange Attractor

Poincare Return Map of a Duffing Oscillator in Chaos

The left upper arm tattoo [above left] is a Strange Attractor (in yin yang form) of a Duffing Oscillator.
Specifically, it is the Poincare Return Map [above right] of the oscillator while in a chaotic dynamic mode.
Scientific Chaos is the unpredictable behavior that deterministic systems sometimes display. A
Strange Attractor is a set of dynamic states toward which a system in chaos evolves. The Duffing
oscillator is a member of a class of periodically forced oscillators with nonlinear elasticity.
The Duffing Oscillator equation has been used to model nonlinear mechanical oscillators, stock
price variations, and deeply trapped star orbits in a spiral galaxy, among other things. The
design was created by plotting several million data points of a simulation by computer.

The following two forearm tattoos were designed as a pair. Together, they represent the only Universal
Language that can exist: Mathematics, the Alpha and Omega of languages. Although only a written
language, it is absolutely identical here as it is on the other side of the Galaxy. Alien
civilizations elsewhere in the Galaxy will agree to its universality. They may use different
symbols to scribe it, but the syntax will be identical to ours, by necessity: There is, after
all, only one dialect of Mathematics. It will be used to initially communicate every time we
make First Contact with a new extrasolar civilization.

Vector Calculus

Vector Calculus (flattened)

The left forearm tattoo [above left] illustrates the two most fundamental theorems of Vector Calculus.
Stokes Theorem is read from the Integral Sign on the left, across the top left loop, through the
Closed Contour Integral Sign, to the lower right. (It says "The surface integral of the curl of vector
function F is equal to the closed contour line integral of F along the perimeter of that
surface.") Gauss' Theorem is read from the Integral Sign on the left, across the lower left
loop, through the Closed Contour Integral Sign, to the upper right. (It says "The volume integral
of the divergence of vector function F is equal to the closed surface integral of F
on the surface of that volume.") Together, they form the symbol Alpha, the first letter of the
Greek alphabet. Vector Calculus was developed by James Clerk Maxwell for the express purpose of
describing and understanding Electromagnetic Fields. A flattened view of the tattoo is above right.

Calculus of Residues

Calculus of Residues (flattened)

The right forearm tattoo [above left] illustrates the calculational tool of "last resort" for Physicists and
Engineers, the Calculus of Residues Theorem. (It says "The closed contour integral of a complex scalar
function F in the complex plane is equal to two pi i (the square root of negative one) times
the sum of the residues of the poles of F enclosed by that contour.") The X in the middle is the
relevant Pole to which the Theorem alludes whose mathematical Residue is physically important to Physicists
and Engineers. The rope represents the relevant contours of integration in the Complex Plane, and form the
symbol Omega, the last letter of the Greek alphabet. Residue theory is part of Complex Analysis, which
involves complex-valued variables and functions, that is, those with real and imaginary parts, and is used
in most branches of Physics and Engineering. Fred Whelan, the tattoo artist, specializes in rope tattoos,
so it seemed natural to use a rope to represent the contours, to add an artistic quality to the design.
A flattened view of the tattoo is above right.

Masonic Field Equations

Vegvisir

The right calf tattoo [above left] is a modified Masonic Symbol. I am a Mason, but Science is my guiding
philosophy in life. So instead of the single letter "G" that is traditionally in the center,
I chose a banner ribbon upon which is written one form of the Einstein Field Equations of General
Relativity to lay across the compass and square. (There are 16 interelated equations built into this
single tensor Calculus equation.) The "G" in the middle of the equation is the Gravitational Constant.
Gravity is the most far reaching of all the physical forces in the Universe, and it fundamentally
describes and controls the very fabric of Space-Time in which we all exist. It represents fundamental
Order in the Universe and treats everything and everyone in it scrupulously fairly. This level of
Fairness and Respect is what I aspire to in my interactions with others.

The left calf tattoo [above right] is Vegvisir, a runic symbol called the Viking Compass or Runic
Compass. Translated from Icelandic, it means “see the way,” “guidepost,” or “direction sign.” For the
Vikings, it was worn or inscribed on the individual, it’s purpose to guide the wearer safely through
storm and fog, to find the way back home. It is not really a Science-themed tattoo, but it is intended
to be viewed in conjunction with the Masonic Field Equations tattoo on my right calf. Together, they
can be read as describing my "Moral Compass," the ethics of Science and the Masonic Brotherhood.

There is one more tattoo that decorates my canvas; It is personal and not related to Science. Yet
another tattoo is in the works and will refer to my love of music. (I've been singing tenor in public
since age 10.) It will be on my outer right forearm and will likely appear on this page eventually, since
music is a mathematical art, and hence deserves to be represented here.

I am what I do. And now, what I "wear" describes what I professionally do. Will there be more tattoos
in my future? Maybe. I am happy with what I have. Perhaps there will be new endeavors that will rival
the passion and interest I already have in Science. I might then consider wearing them on my sleeve, too.

I have some advice for those who might consider a tattoo of their own someday. Take your time, lots of time.
Be very sure it is what you want, because you'll be stuck with it forever. Design your own, or have one
designed specifically for you by a good artist. The tattoo should be special to you personally. Go to a
reputable (read, expensive) tattoo artist. It'll be worth the time and money. A good tattoo artist will
not ink just any old crap on your skin; He'd rather lose a client than permanently ink a terrible
design. The size of the tattoo should be tasteful (small, generally). It's placement should be
appropriate. Stay away from tattoos on your head or neck. They can not be covered for those special
occassions that may so require it, such as weddings or job interviews.